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Section: New Results

Interacting Markov chain Monte Carlo methods

Participants : Bernard Bercu, Anthony Brockwell, Pierre Del Moral, Arnaud Doucet.

This new line of research is mainly concerned with the design and the analysis of a new class of interacting stochastic algorithms for sampling complex distributions including Boltzmann-Gibbs measures and Feynman-Kac path integral semigroups arising in physics, in biology and in advanced stochastic engineering science. These interacting sampling methods can be described as adaptive and dynamic simulation algorithms which take advantage of the information carried by the past history to increase the quality of the next series of samples. One critical aspect of this technique as opposed to standard Markov chain Monte Carlo methods is that it provides a natural adaptation and reinforced learning strategy of the physical or engineering evolution equation at hand. This type of reinforcement with the past is observed frequently in nature and society, where beneficial interactions with the past history tend to be repeated. Moreover, in contrast to more traditional mean field type particle models and related sequential Monte Carlo techniques, these stochastic algorithms can increase the precision and performance of the numerical approximations iteratively. The origins of these interacting sampling methods can be traced back to a pair of articles  [35] , [36] by P. Del Moral and L. Miclo. These studies are concerned with biology-inspired self-interacting Markov chain models with applications to genetic type algorithms involving a competition between the natural reinforcement mechanisms and the potential attraction of a given exploration landscape.

In 2008-2009, these lines of research have been developed in three different directions :


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